Symmetric and non-symmetric quantum Capelli polynomials

被引：0
|
作者：
Knop, F
机构：
来源：
COMMENTARII MATHEMATICI HELVETICI | 1997年 / 72卷 / 01期
关键词：
symmetric polynomials; Capelli identity; Macdonald polynomials; difference operators; Hecke algebras;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce families of symmetric and non-symmetric polynomials (the quantum Capelli polynomials) which depend on two parameters q and t, They are defined in terms of vanishing conditions, In the differential limit (q = t(alpha) and t --> 1) they are related to Capelli identities. It is shown that the quantum Capelli polynomials form an eigenbasis for certain q-difference operators. As a corollary, we obtain that the top homogeneous part is a symmetric/non-symmetric Macdonald polynomial. Furthermore, we study the vanishing and integrality properties of the quantum Capelli polynomials.
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页码：84 / 100
页数：17
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